Answer:
Step-by-step explanation:
As of today, Chase has won 18 out of 30 games against his brother. The percentage of games that he has won as of today is
18/30 × 100 = 60%
In order to get 75% wins, let the number of games would be x. Then
(18 + x)/(30 + x) × 100 = 75
100(18 + x) = 75(30 + x)
1800 + 100x = 2250 + 75x
100x - 75x = 2250 - 1800
25x = 450
x = 450/25 = 18
chase has to win 18 games in a row.
In order to get 90% wins, let the number of games would be y. Then
(18 + x)/(30 + x) × 100 = 90
100(18 + x) = 90(30 + x)
1800 + 100x = 2700 + 75x
100x - 75x = 2700 - 1800
25x = 900
x = 900/25 = 36
chase has to win 36 games in a row in order to have a 90% winning record.
(18 + x)/(30 + x) × 100 = 100
100(1800 + x) = 100(30 + x)
1800 + 100x = 3000 + 100x
100x - 100x = 3000 - 1800
Therefore, it is impossible to for chase to reach a 100% winning record because he has already had some losses.
2) for a wining record of 90, the total number of games played is
30 + 36 = 66 games and the total number of wins was 18 + 36 = 54
In order to get 55% losses, let the number of games would be z. Then
(54 + z)/(66 + z) × 100 = 55
100(54 + z) = 55(66 + z)
5400 + 100z = 3630 + 55z
100z - 55z = 3630 - 5400
45z = - 1770
z = - 1770/45 = - 40
chase has to lose 40 games in a row in order to drop down to a winning record below 55% again.
